Adaptive control designs for control-based continuation in a class of uncertain discrete-time dynamical systems

2020 ◽  
Vol 26 (21-22) ◽  
pp. 2092-2109
Author(s):  
Yang Li ◽  
Harry Dankowicz
Keyword(s):  
Adaptive Control ◽  
Discrete Time ◽  
Closed Loop ◽  
Control Strategies ◽  
Open Loop ◽  
Numerical Continuation ◽  
Pole Placement ◽  
Control Input ◽  
Loop Dynamics ◽  
Reference Input

This article proposes a methodology for integrating adaptive control with the control-based continuation paradigm for a class of uncertain, linear, discrete-time systems. The proposed adaptive control strategies aim to stabilize the closed-loop dynamics with convergence toward a known reference input, such that the dynamics approach the open-loop fixed point if the reference input is chosen to make the steady-state control input equal 0. This enables the tracking of a parameterized branch of open-loop fixed points using methods of numerical continuation without specific knowledge about the system. We implement two different adaptive control strategies: model-reference adaptive control and pole-placement adaptive control. Both implementations achieve the desired objectives for the closed-loop dynamics and support parameter continuation. These properties, as well as the boundedness of system states and control inputs, are guaranteed provided that certain stability conditions are satisfied. Besides, the tuning effort is significantly reduced in the adaptive control schemes compared with traditional proportional–derivative controllers and linear state-space feedback controllers.

Model Based Control of Laminar Wake Using Fluidic Actuation

2010 ◽  
Vol 5 (4) ◽  
Author(s):  
Imran Akhtar ◽  
Ali H. Nayfeh
Keyword(s):  
Dynamical System ◽  
Stokes Equations ◽  
Control Function ◽  
Practical Importance ◽  
Nonlinear Damping ◽  
Open Loop ◽  
Pole Placement ◽  
Cylinder Surface ◽  
Control Input ◽  
Laminar Wake

Control of fluid-structure interaction is of practical importance from the perspective of wake modification and reduction of vortex-induced vibrations (VIVs). The aim of this study is to design a control to suppress vortex shedding. We perform a two-dimensional simulation of the flow past a circular cylinder using a parallel Computational Fluid Dynamics (CFD) solver. We record the velocity and pressure fields over a shedding cycle and compute the proper orthogonal decomposition (POD) modes of the divergence-free velocity and pressure, respectively. The Navier–Stokes equations are projected onto these POD modes to reduce the dynamical system to a set of ordinary-differential equations (ODEs). This dynamical system exhibits a limit cycle with negative linear damping and positive nonlinear damping. The reduced-order model is then modified by placing a pair of suction actuators and applying a control strategy using a control function method. We use the pressure POD mode distribution on the cylinder surface to optimally locate the actuators. We design a controller based on the linearized system and make it positively damped using pole-placement technique. The control-input settles to a constant value, suggesting constant suction through the actuators. We validate the results using CFD simulations in an open-loop setting and observe suppression of the hydrodynamic forces acting on the cylinder.

Stability analysis of a discrete-time system with a variable-, fractional-order controller

2010 ◽  
Vol 58 (4) ◽  
pp. 613-619 ◽  
Author(s):  
P. Ostalczyk
Keyword(s):  
Stability Analysis ◽  
Fractional Order ◽  
Discrete Time ◽  
Closed Loop ◽  
Control Strategies ◽  
Discrete Time System ◽  
Time System ◽  
Matrix Condition Number ◽  
Fractional Order Controller ◽  
Matrix Condition

Stability analysis of a discrete-time system with a variable-, fractional-order controllerVariable, fractional-order backward difference is a generalisation of commonly known difference or sum. Equations with these differences can be used to describe a variable-, fractional order digital control strategies. One should mention, that classical tools such as a state-space description and discrete transfer function cannot be used in the analysis and synthesis of such a type of systems. Equations describing a closed-loop system are proposed. They contain square matrices imitating the action of matrices in the system polynomial matrix description. This paper focuses on the stability analysis of a closed-loop SISO linear system with a controller described by the equations mentioned. A stability condition based on a transient denominator matrix condition number is proposed. Investigations are supported by two numerical examples.

An L1 adaptive closed-loop guidance law for an orbital injection problem

2009 ◽  
Vol 223 (6) ◽  
pp. 753-761 ◽  
Author(s):  
J Roshanian ◽  
M Zareh ◽  
H H Afshari ◽  
M Rezaei
Keyword(s):  
Closed Loop ◽  
Adaptive Strategy ◽  
Analytical Form ◽  
Open Loop ◽  
Control Input ◽  
Guidance Law ◽  
Non Linear ◽  
Non Linear System ◽  
Orbital Injection

The current paper presents the determination of a closed-loop guidance law for an orbital injection problem using two different approaches and, considering the existing time-optimal open-loop trajectory as the nominal solution, compares the advantages of the two proposed strategies. In the first method, named neighbouring optimal control (NOC), the perturbation feedback method is utilized to determine the closed-loop trajectory in an analytical form for the non-linear system. This law, which produces feedback gains, is in general a function of small perturbations appearing in the states and constraints separately. The second method uses an L1 adaptive strategy in determination of the non-linear closed-loop guidance law. The main advantages of this method include characteristics such as improvement of asymptotic tracking, guaranteed time-delay margin, and smooth control input. The accuracy of the two methods is compared by introducing a high-frequency sinusoidal noise. The simulation results indicate that the L1 adaptive strategy has a better performance than the NOC method to track the nominal trajectory when the noise amplitude is increased. On the other hand, the main advantage of the NOC method is its ability to solve a non-linear, two-point, boundary-value problem in the minimum time.

scholarly journals Control of Flexible Manipulator Systems

1996 ◽  
Vol 210 (2) ◽  
pp. 113-130 ◽  
Author(s):  
M O Tokhi ◽  
A K M Azad
Keyword(s):  
Closed Loop ◽  
Control Strategies ◽  
Open Loop ◽  
Flexible Manipulator ◽  
Closed Loop Control ◽  
Loop Control ◽  
Acceleration Feedback ◽  
Low Pass ◽  
Input Torque ◽  
Collocated Control

This paper presents an investigation into the development of open-loop and closed-loop control strategies for flexible manipulator systems. Shaped torque inputs, including Gaussian-shaped and low-pass (Butter-worth and elliptic) filtered input torque functions, are developed and used in an open-loop configuration and their performance studied in comparison to a bang-bang input torque through experimentation on a single-link flexible manipulator system. Closed-loop control strategies that use both collocated (hub angle and hub velocity) and non-collocated (end-point acceleration) feedback are then proposed. A collocated proportional and derivative (PD) control is first developed and its performance studied through experimentation. The collocated control is then extended to incorporate, additionally, non-collocated feedback through a proportional integral derivative (PID) configuration. The performance of the hybrid collocated and non-collocated control strategy thus developed is studied through experimentation. Experimental results verifying the performance of the developed control strategies are presented and discussed.

A Static Anti-Windup Compensator Design Technique for Robust Regional Pole Placement

2006 ◽  
Author(s):  
Brandon Hencey ◽  
Andrew Alleyne
Keyword(s):  
Closed Loop ◽  
Linear Time ◽  
Pole Placement ◽  
Linear Matrix ◽  
Test Bed ◽  
Hydraulic Test ◽  
Linear Time Invariant ◽  
Loop Dynamics ◽  
Performance Deterioration ◽  
Time Invariant

This paper develops a new method of designing anti-windup compensators using the concept of robust pole placement using linear matrix inequality (LMI) regions. The anti-windup problem seeks to minimize the closed loop performance deterioration due to input nonlinearities such as saturation for a given linear time-invariant plant and controller. Existing LMI-based anti-windup synthesis techniques do not explicitly provide a method to account for robust pole placement. This paper suggests a LMI-based method that not only attempts to minimize performance deterioration, but also explicitly restricts the anti-windup closed loop dynamics to an admissible set. Finally, the techniques discussed in this paper are demonstrated on a hydraulic test bed.

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